title: Assessing variance components in multilevel linear models using approximate Bayes factors: A case study of ethnic disparities in birthweight.
abstract: Racial/ethnic disparities in birthweight are a large source of differential morbidity and mortality worldwide and have remained largely unexplained in epidemiologic models. We assess the impact of maternal ancestry and census tract residence on infant birth weights in New York City and the modifying effects of race and nativity by incorporating random effects in a multilevel linear model. Evaluating the significance of these predictors involves the test of whether the variances of the random effects are equal to zero. This is problematic because the null hypothesis lies on the boundary of the parameter space. We generalize an approach for assessing random effects in the two-level linear model to a broader class of multilevel linear models by scaling the random effects to the residual variance and introducing parameters that control the relative contribution of the random effects. After integrating over the random effects and variance components, the resulting integrals needed to calculate the Bayes factor can be efficiently approximated with Laplace's method.
authors.affiliation: Department of Biostatistics, Vanderbilt University School of Medicine S-2323 Medical Center North, 1161 21st Avenue South Nashville, TN 37232-2158, b.saville@vanderbilt.edu.
authors.forename: Benjamin R
authors.initials: BR
authors.lastname: Saville
authors.forename: Amy H
authors.initials: AH
authors.lastname: Herring
authors.forename: Jay S
authors.initials: JS
authors.lastname: Kaufman
keywords: Bayes factors; Laplace approximation; hierarchical; multilevel linear model; variance components